Not sure what that is. Has a valve like look to it doesn't it. Looks more like a suction valve though. Maybe if the fuel pressure on the suction side of the secondary pump drops below 0.5 bar this opens up to provide additional fuel volume from the return line. Just guessing here.

Not listed in the parts list. Appears to be part of the secondary fuel pump assembly.

I find that you can push a thin nylon line through these hoses. Like a fishing line. Maybe put one in from the connector on top of the cooler and see if it makes it past that H connection. I used the fishing line to pull a rubber plug through the lines in the engine bay of my TDv6 to wipe the inside of the lines clean.

It may be a pressure relief valve. For example let’s say the tank pump over pressurises its delivery … that valve may open and vent fuel into the return loop and back into the tank , protecting parts further up stream. V8 or else ...